# Adaptive First Principles Model for the CAS-OB Process for Real-Time Applications

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## Abstract

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^{®}CENIT™ framework. The overall model can be regarded as a hybrid digital twin, where a first principles model is adapted in real time using process measurements. The system also includes user interfaces for operators where process predictions can be followed, and suggested optimised inputs are presented. The system has been deployed at two refining stations at SSAB Europe OY in Raahe, Finland. The optimized suggestions for oxygen and scrap are presented to the operators in the graphical user interface. A projected temperature profile is calculated into the near future using the planned operational procedure as well as the projected temperature profile using optimised inputs. Both profiles are displayed in the user interface. Based on these trajectories, the operator can decide on whether to follow the nominal trajectory, or the recommendation from the optimisation This will help the operators make better decisions, which in turn reduces the number of rejected heats in the CAS-OB process.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Control Volumes and State-Space Variables

#### 2.1.1. Liquid Steel Phases

#### 2.1.2. Slag Phase

#### 2.1.3. Gas Phase

#### 2.1.4. Ladle

#### 2.1.5. Bell

#### 2.2. Chemical Reactions

#### 2.2.1. Dissolution of Added Material

#### 2.2.2. Free Surface Reactions

#### 2.2.3. Slag-Metal Interface Reactions

#### 2.3. Heat Transfer

#### 2.4. Mass and Energy Balances

#### 2.4.1. Free Surface

#### 2.4.2. Liquid Steel

#### 2.4.3. Gas Phase

#### 2.4.4. Model Summary

#### 2.5. Recursive Parameter and State Estimation

#### 2.6. Real-Time Optimization

## 3. Results

#### 3.1. Model Agreement with Process Data

#### 3.2. Recursive Estimation

#### 3.3. Industrial Use and Application

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BOF | Basic Oxygen Furnace | |

CAS-OB | Composition Adjustment by Sealed | |

argon-bubbling with Oxygen Blowing | ||

CFD | Computational Fluid Dynamics | |

MPC | Model Predictive Control | |

NMPC | Nonlinear Model Predictive Control | |

Symbol | Description | Unit |

${m}_{i}$ | Mass of component i | kg |

${c}_{i}$ | Concentration of component i | mass fraction |

${M}_{i}$ | Specific molar mass of component i | kg/kmol |

${w}_{i}$ | Mass flow of component i | kg/s |

${R}_{j}$ | Reaction rate of reaction j | kmol/s |

${T}_{k}$ | Temperature of control volume k | K |

${Q}_{k-l}$ | Heat transfer between control volumes k and l | W |

$C{p}_{i}$ | Heat capacity of component or control volume | J/(kg K) |

${S}_{k}$ | Surface area of k | m${}^{2}$ |

${\alpha}_{k}$ | Heat transfer coefficient for k | W/(m${}^{2}$ K) |

Subscript notation | ||

f | Free surface control volume | |

L | Liquid control volume | |

$Li$ | Inner section of Ladle control volume | |

$Bi$ | Inner section of Bell control volume | |

s | Slag control volume | |

f–L | From Free surface to Liquid control volumes | |

L–f | From Liquid to Free surface control volumes | |

$in$ | Material addition |

## References

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**Figure 3.**Histogram showing improvement of prediction errors by estimation on the final temperature estimates in the heat.

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**MDPI and ACS Style**

Linnestad, K.; Ollila, S.; Wasbø, S.O.; Bogdanoff, A.; Rotevatn, T.
Adaptive First Principles Model for the CAS-OB Process for Real-Time Applications. *Metals* **2021**, *11*, 1554.
https://doi.org/10.3390/met11101554

**AMA Style**

Linnestad K, Ollila S, Wasbø SO, Bogdanoff A, Rotevatn T.
Adaptive First Principles Model for the CAS-OB Process for Real-Time Applications. *Metals*. 2021; 11(10):1554.
https://doi.org/10.3390/met11101554

**Chicago/Turabian Style**

Linnestad, Kasper, Seppo Ollila, Stein O. Wasbø, Agne Bogdanoff, and Torstein Rotevatn.
2021. "Adaptive First Principles Model for the CAS-OB Process for Real-Time Applications" *Metals* 11, no. 10: 1554.
https://doi.org/10.3390/met11101554